Geodesic
Bijection between trees in Stanley character formula and factorizations of a cycle
Karolina Trokowska1 ; Piotr Śniady2
1(no affiliation)
2Institute of Mathematics, Polish Academy of Sciences
The electronic journal of combinatorics, Tome 31 (2024) no. 1
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Stanley and Féray gave a formula for the irreducible character of the symmetric group related to a multi-rectangular Young diagram. This formula shows that the character is a polynomial in the multi-rectangularcoordinates and gives an explicit combinatorial interpretation for its coefficients in terms of counting certain decorated maps (i.e., graphs drawn on surfaces). In the current paper we concentrate on the coefficients of thetop-degree monomials in the Stanley character polynomial, which corresponds to counting certain decorated plane trees. We give an explicit bijection between such trees and minimal factorizations of a cycle.
DOI : 10.37236/11577
Classification : 05C38, 05C70, 05A19, 05C05, 05E10, 20C30
Mots-clés : partitions of rectangular shape, irreducible complex characters, symmetric groups, normalized characters, hook lengths, Young diagrams

Karolina Trokowska  1   ; Piotr Śniady  2

1 (no affiliation)
2 Institute of Mathematics, Polish Academy of Sciences 
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     title = {Bijection between trees in {Stanley} character formula and factorizations of a cycle},
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     year = {2024},
     volume = {31},
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Karolina Trokowska; Piotr Śniady. Bijection between trees in Stanley character formula and factorizations of a cycle. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/11577

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